They've lost a lot of their oversight power because so many teachers and school administrators, and their relatives, are running for and winning seats.
One year, the Willingboro NJ school board was made up entirely of teachers or teacher-relatives, with the exception of the lawyer who was orchestrating the whole thing.
That's not the case in Kentucky. Here relatives of teachers, administrators and/or any employees of the school system are not allowed to run for the school board.
Personally, I have always thought that was a bad idea. I grew up in a VERY rural area where the schools were the largest employer in the county. It was hard to find anyone decent that was not connected to the school system in some way.